Tree-Independent Dual-Tree Algorithms

Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1435-1443, 2013.

Abstract

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.

Related Material

@InProceedings{pmlr-v28-curtin13,
title = {Tree-Independent Dual-Tree Algorithms},
author = {Ryan Curtin and William March and Parikshit Ram and David Anderson and Alexander Gray and Charles Isbell},
booktitle = {Proceedings of the 30th International Conference on Machine Learning},
pages = {1435--1443},
year = {2013},
editor = {Sanjoy Dasgupta and David McAllester},
volume = {28},
number = {3},
series = {Proceedings of Machine Learning Research},
address = {Atlanta, Georgia, USA},
month = {17--19 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v28/curtin13.pdf},
url = {http://proceedings.mlr.press/v28/curtin13.html},
abstract = {Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.}
}

%0 Conference Paper
%T Tree-Independent Dual-Tree Algorithms
%A Ryan Curtin
%A William March
%A Parikshit Ram
%A David Anderson
%A Alexander Gray
%A Charles Isbell
%B Proceedings of the 30th International Conference on Machine Learning
%C Proceedings of Machine Learning Research
%D 2013
%E Sanjoy Dasgupta
%E David McAllester
%F pmlr-v28-curtin13
%I PMLR
%J Proceedings of Machine Learning Research
%P 1435--1443
%U http://proceedings.mlr.press
%V 28
%N 3
%W PMLR
%X Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.